ee313_exam2_fall2002

ee313_exam2_fall2002 - BB 313 Midterm Exam 2 Name This exam...

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Unformatted text preview: BB 313 Midterm Exam 2 November 16, 2001 Name This exam consists of 4 equal—weight questions. Show all of your work in order to receive full credit. Attached to this test are the following tables from the text: 1) Laplace Transform Pairs 2) Laplace Transform Operations 3) Z—Transform Pairs 4) Z—Transform Operations Formula: \x / 1 . , r (g " f {'1 p * fl ; v x’ 3 \ ‘ ' ‘~' inf/V yin r / I JY/ 7 j 7 ‘1 0 ' ’7 G u " f- a; Question 1. Consider the signals f (t) and g(t) shown in the figures below. :7“ gm f(t) ' l g (a) By direct integrationefindlherLaplace transform and region of convergence of f (t) . f (b)rFind the Laplace transform and region of convergence of g(t). :3 (c) Find the Laplace transform of g( 0.St)and sketch a plot of g( O.5t)vs. t. .. r «:::>:v.::> r a . - . «A: T. (0; H11}: '2: -_> 5:; /‘ gt '— ~ ‘3. at —_ 3 a,“ ; .. I _ E f _. .311 “1 m w \ e A) J! :i t» ,3, 39 3- ” e. 7131 ‘ui a 7 O 2‘” A <41; ”‘ f / J "’ Wit) ., Co ‘ 3 ,0 " u ’5va ‘ 1 A1 I! , i ‘1! , - if”; 7.: {a Few; a PM :-— *3 w\’: L‘ ._7 z ‘1. .. g ; l I: ?" - e? ‘ W F( 1L > i .2 a l w i '1 —- «1 “ n .1", ’ k __ ‘ "v V‘ -~ ~~~~~~~ ~ "" “I?” ",1 . _ . t “l (C) 1... r L .3" 4, ,‘z; . : 2 OIKQS/! v I _ g . .-. _-. a _ g u fix F K r x . ‘ 3 " ‘; - a: C 7 .4. ‘ é; '\' {n 2 M”. W“ M :: l ‘ 3 i 4.3} L» .— 4:. g ’ T if -’ 5 n u 3. 33—) @ c l 3 ~ 11‘ - n.1,“ I V ‘. “’p ‘ fl 0") "" l. x, J A. 7. z if! ;‘ ‘Is ‘ e > [ll , J €— 1“ .f E j _ o ‘ 2 '9 Z '— , A f B J ,z"“\.\ ‘ K K ‘ . \ ,r . . . . . . . . . {Questlo/m‘Z. Thie transfer function of a continuous-time linear tlme-lnvanant system 15 \given 'y / \\,\\/L\M////f _ [1(5) = ___§¥2)_ _ (s+1)(s +2s+2) {O (a) Show a block diagram of the system in cascade form. ‘ (b) Realize the system in cascade form using integrators, multipliers, and adders. F\{S‘\’ orclPV 3 xi“; EM. 8 k. W 126,: A fig {1 1:? K i ’1’ \E («A : r? W. _ .\‘V‘;V."L > .\‘ Question 3. Consider a discrete—time system described by the difference equation 4y(k)+ 43(k — 1) +y(k— 2) =f(k- 1), k 20. x w: 20 (a) Find the response y( k) of the system with input f (k) = 3k u(k) and initial conditions y(—1)= 0 and y(—2)= 1. 5 (b) What is the transfer function of the system? (a) wmw HL'\\((Z')+‘Z'1Y(2)41 _. i'Fc-L) \ .\ \ - k 7' fi‘ — 3. {H + ‘-\7_"+z‘1 )Wz; = 1 Lit—g3 _ A, - 2‘3 awful—WW) __ 33.17:. z‘lk‘d12+\'\1*iv\al> ' 1—3 = 7. zeta/’11 " (1—3 My“; /‘:\ 51,3 )sz’rl" % 1 w \__ m \ k3 W0) 3‘. T vii—L” ~r ZJf l, J : dbl“); \Z‘r“ a.“ 1’3": t'Zszi : O 104—17 ‘ _ l \ ’fflffl \ ,.—”3' )L\ 1 \ O i1. ‘L/i ‘fl-’ ’ 7. 2,) L 1 3 1 - n. \ ‘\S-2..,.5 — ~ L24; S \ W‘M\ \ .1 z, / as _ \ —~ " (1:531, 1”; , V " r 4 \h’H‘iCLfln \ Arr/0‘ ‘ EO‘ZWS +0.(0L\AQ~(11 I .J My ’1 q \ h c —\ h _"\ ¢\ \RV/O 2 "mow (37% o.\bh\z) — 0.3‘\2) J ) x” i L} x» Question‘4. The transfer function HQflEfgdficreteZtime LTI system is given by My , ” ' 3 ~ a.» r (a) Is the system stable? Why or why not. (b) Find the frequency response of the system. (c) Find the system response y( k) to the input f (k) = cost—1: k) for k 2 0. (d) Is the frequency response periodic? Why or why not. NP . . L63 Yes bar 003C it: PM: 1- 0.6 M'ea mswe flu; omit curate» o§ m (manta-M Pkmm,‘ _ .jL ‘JL ‘ ' , ' ' J), m We: 3: e} + 0.9 ._ W mg 4 _ o. 5 + ~ sue—0.. fir” .- o. 5 8 (C) \\-\K€5JL) = <Qo§jL+o§3>L +<SWQL>1 LCDSJL’O'S71 + (Sm .17.):- gz/‘A lid/K 'L/ t '- Los‘JL + \xbwsfi.+ O.(o'~\ + min. W \‘CoSIJL— cosh. + 02.5 + Smle Lb C0341 3? -co~5.52.~: L25 ’ 4 MW” — 5 JL \ \ «x 40m“‘ j)“ MW \ cosh—0.5 / t V __ T For "x ‘0- “ ‘3’ *3 ‘1 \ \ 3W1 ‘ ’ ,-\’ ’"’ - mud - /: O'Bqa)’ L Hue > - mm- \ OR ) \ 0‘3 -‘_— -\.138 Md- : #95:” Mo = \HE- r2”: CWT/2““ '38) .(L/ “as we :. JJ€fl , 1'05: “but 0 3 CW {r L“??? ARUWQV‘HA HSPD'NNL”: oiwoqfi X10 \iC' ...
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This note was uploaded on 02/09/2010 for the course EE 313 taught by Professor Cardwell during the Fall '07 term at University of Texas.

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ee313_exam2_fall2002 - BB 313 Midterm Exam 2 Name This exam...

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